Twistreflector



Dec. 15, 1964 P. W. HANNAN ETAL Filed Jan. 5, 1961 5 Sheets-Sheet 1REFLECTING SURFACE ELEMENTS 3 v INCIDENJ' RAY REFLECTED RAY Q |2 0N KPOLARIZATION 1 WITH ORDINAR REFLECTOR l I /REFLECTED POLARIZATION lbOBLIQUE INCIDENCE FIG. I

W. Hcmnon Peter Henry Jusik Kenneth B. Woodard,

INVE

NTORS.

ATTOR YS.

1964 P. w. HANNAN ETAL 3,161,879

TWISTREFLECTOR 3 Sheets-Sheet 2 Filed Jan. 5, 1961 COMPONENT .L TOELEMENTS COMPONENT ll N m T A z R A lo P TO ELEMENTS COMPONENT .L T0

ELEMENTS SHIFTED m PHASE BY A HALF WAVE LENGTH RESULTANT POLARIZATION llTO ELEMENTS\ FIG. 2

METAL SURFACE E- KVVm METAL WIRES SHORT CIRCUIT .1. COMPONENT MM s 0 .MTY m mm m n V O OWW T 6 m w m n 666 Y B W U C S m m C m o klw A 4cos@FIG. 3

ll COMPONENT 3b EQUIVALENT TRANSMISSION LINES 'of an incident linearpolarized wave. between the metal sheet and wire elements the spacinggiven in FIGURE 1(a).

United States Patent "cc 3,161,879 TWISTREFLECTOR Peter W. Hannan, GreatNeck, and Henry Jasik, Flushing, N.Y., and Kenneth B. Woodard, BaskingRidge, N.J., assignors, by mesne assignments, to the United States ofAmerica as represented by the Secretary of the Army Filed Jan. 5, 1961,Ser. No. 80,961

1 Claim. (Cl. 34318) This invention relates to means for reflectingelectromagnetic waves and particularly to a reflector which bothreflects and twists the polarization of an incident wave by 90.

' It is the object of the invention to provide a reflector whichcombines the properties of reflection and 90 rotation of polarizationwhile oflering both a wideband using'a completely reflecting metal sheetand a series of conducting parallel wire elements positioned in front ofthe reflecting sheet and aligned at 45 to the polarization For airspacing is in the midrange between one fourth and one halfguidewavelengths, wavelengths in an equivalent transmission line whichis greater than free space wavelength by the factor l/cos 9, where 6 isthe angle of incidence. By

the term midrange it is intended to exclude spacing which issubstantially one-quarter or one-half wavelength. The spacing may alsovary by added multiples of one-half guide-wavelengths. The wire diameteris made substantially smaller'than wire-to-wire spacing and thewire-towire spacing small compared to the wavelength of energy to bereflected,

The structure and operation of apparatus embodying the principles of thepresent invention will be more clearlyunderstood from a consideration ofthe following de- FIGURE 3 shows a cross-section of a rudimentary'FIGURE 5 shows a modification of the embodiment e of the invention shownin FIGURE 4 in which the wire elements are supported by a dielectric.

Referring now to FIGURE 1, the twistreflector comprises a metalcompletely reflecting sheet 10 behind a series of parallel metalelements 12 aligned at 45 to the polarization of an incident linearpolarized electromagnetic wave. The elements are such that the componentof the wave which is polarized parallel to the wires is shifted a halfwave in phase relative to the component polarized perpendicular to thewires. polarization of the reflected wave being twisted by 90, as isexplained below.

" The-basic geometry of the twistreflector action is also shown inFIGURE 1. The case of normal incidence is of the elements on theincident wavefront (plane perpen- This results in the If the incidentpolarization is at .two' components.

is not twisted the wires. .circuit effect may be obtained with lessclosely spaced 3,lfil,879 Patented Dec. 15, 1964 equal in magnitudebecause the incident polarization is specified as being at 45 to theprojection of the elements, as discussed above. After reflection fromthe twistreflector, these two components are unchanged in magnitude, butthe phase of one has been shifted a half wavelength relative to theother by the elements. As shown, the resultant of these two componentsis a wave equal in magnitude to the incident one, but whose polarizationis twisted by 90 i The essential property of the elements is thehalf-wavelength'phase shift of one component relative to the other.Elements or materials which are anisotropic are capable of achievingthis. Some possible elements include metal or dielectric strips, wires,dipoles and slots. 7

A twistreflector may be made of a metal surface and metal wiresinvolving wires which completely reflect the component polarizedparallel to their projection and completely transmitting theperpendicular component. This situation may be approached by making thewire spacing very small compared to a wavelength, and the wire diametermuch less than the spacing. In order to shift the phase of the parallelcomponent by a half wavelength relative to the perpendicular component,the wires are located a quarter wavelength ahead of the metal surface.

' The cross-section of this design is drawn in FIGURE 3. Also shown arethe equivalent transmission lines for the The transmission line for theperpendicular component is short-circuited by the metal surface, whilethe transmission line for the parallel component is short-circuited bythe wires a quarter wavelength ahead. Thus the wave reflected fromtheseshort circuits has a half wavelength further to travel in the caseof perpendicular polarization than it does for parallel polarization.

It may be noted in FIGURE 3 that the dimensions are given in terms ofwavelength divided by cos 6. This is because a wave incident at an'oblique'angle has an effective wavelength in the equivalenttransmission lines (guide wavelength) which is greater than thefree-space wavelength by the factor l/cos 9. Thus, if the twistreflectoris intended to operate at oblique incidence, the distance from the wiresto the metal surface should be M4 cos 9, in order that the two reflectedcomponents be a half guidewavelen gth out of phase.

The simple design just described performs perfectly at 'the frequencyand angle of incidence for which it is designed. However, it is apparentthat at another frequency or incidence angle the wire layer is no longera quarter guide-wavelength from the metal surface. This will result inthe reflected wave having a component which It will be shown however howa modification of the twistreflector enables it to achieve nearlyperfect twisting over a range of frequency and angle of incidence.

The twistreflector described above achieves the desired half-wavelengthphase shift between the two components by having actual short circuitsfor the two components which are a quarter wavelength apart. The shortcircuit for the parallel component is obtained by close spacing ofHowever, it has been found that the short wires which do not completelyreflect the parallel component. In this case, the metal surface reflectsthat part of the parallel component not reflected by the wires, inaddition to reflecting all of the perpendicular component. The .wiresmust be located more than a quarter wavelength away from the metalsurface in order that the effective short circuit for the parallelcomponent be still a quarter wavelength away. To illustrate theeffective or apparent short circuit, reference is made to FIGURE 4. Alsoshown are the equivalent transmission lines for the two components. Thewires are seen to introduce inductive (negative) susceptance across thetransmission line for the parallel component. The value of thissusceptance is given by the following approximate formula:

37 35 cos 9 In 1rD B susceptance of the wires. Y =admittance of freespace. t=wavelength in free space. S=spacing between wire centerlines.:angle of incidence.

D diameter of wires.

Y' input admittance for component whose electric field is perpendicularto the wires.

Y=input admittance for component whose electric field is parallel to thewires.

By standard transmission-line analysis, the input admittance of the twolines at a reference plane through the wires is:

Y 21rL cos 9 if ctn (3) L distance from metal surface to wire centerlinein the all-metal design.

Substituting (3) and (4) in (2), and solving for B /Y yields thefollowing formula:

B 41rL cos 9 Y0 2 csc A If this relationship is satisfied, then thetwistreflector performs as intended. It can be seen that the susceptanceB /Y may take any value from infinity to 2. For negative susceptance,corresponding to inductive wires, the distance from the wires to themetal surface may be any value between one-quarter guide-wavelength andone-half guide-wavelength. (If the elements had positive susceptance,i.e, were capacitive, the distance would be between zero and one-quarterguide-wavelength. However, such elements cannot be made from metalwires; thin dielectric wires would be required.)

Both the quarter and the half guide-wavelength distances for theinductive case correspond to a value of minus infinity for B Y andrequire very closely spaced wires. The quarter guide-Wavelength case isthe simple design illustrated in FIGURE 3, while the halfguidewavelength case is a resonant one, and consequently yieldsextremely narrow-band and narrow-angle performance. A distance ofthree-eighths guide-wavelength corresponds to the smallest possiblemagnitude of B /Y the value at this point is B /Y =2. This design yieldsthe greatest allowable spacing between wires, as may be seen fromFormula 1. It should be mentioned that other ranges of greater distancesare also possible (greater by one-half guide-wavelength), but it isusually desirable to choose the small one in order to obtain minimumsize and best performance.

Substituting the expression for the susceptance of the wires (1) into(5) yields the single formula which determines the relationship betweenthe various dimensions and the characteristics of the incident wave forperfect operation of the general twistreflector:

2 080 (47rL cos G 1 A S cos 9 In (:2)

For any specified values of frequency and angle of incidence, a range ofvalues for L, S and D are allowable, with any two then determining thethird.

As indicated above it is desired to obtain a twistreflector whichperforms well over a range of values of the frequency and the angle ofincidence. We will define an optimum performance the condition whereby afirstorder small change of frequency or incidence angle causes adeparture from perfect polarization twisting of only seeond-ordersmallness. This, it has been found, may be determined by differentiatingFormula 6 with respect to and 9. In both cases, this gives the followingrelationship:

All the solutions of this equation which yield inductive (negative)susceptance in Formula 5 yield an optimum design. However, the lowestorder solution is the best because the twistreflector performanceremains good over the widest range of frequency and incidence angle.This solution is:

- i 358 or L=% g (8 Thus in the optimum design, the distance from thewires to the metal surface is directly determined by the fre quency andangle of the incident wave. It should be noted that, since Equation 7was obtained in both cases, the resulting single optimum design issimultaneously optimum for both frequency changes and changes of angleof incidence. Values approximating the optimum solution will of courseprovide acceptable results.

Substituting the value in Formula 8 into Formula 5 yields:

This inductive susceptance is close to the minimum possible value (2.00)noted in the previous section. Therefore the optimum design has a numberof wires which is close to the minimum possible.

Substituting the value in Formula 9 into Formula 1 yields:

as wire spacing is increased, the diameter can be increased in such away as to maintain the equality given by Formula 10. The only limit onthis process is that the wire spacing be not too large a fraction of awavelength, in order that Formula 1 for wire susceptance be a goodapproximation, and to preclude the possibility of a coherent set ofdiffracted waves. If the spacing between wires is kept less than aquarter wavelength, the formulas are accurate enough for most purposes,and diffracted waves are far from existence. Within this limitation, andthe relationship imposed by Formula 10, the wire screen dimensions maybe chosen for constructional convenience. This is also true for thegeneral design, as seen in Formula 6.

The twistreflector designs so far described are constructed of roundmetal wires and metal sheet: both materials are readily obtainable.However, for many if not all practical applications suitable means ofsupporting the wires must be determined. As a feature of this inventiona dielectric material of very low dielectric constant (K) is used tofill most of the space between the metal surface and the wires, and avery thin dielectric sheet used to house the wires. Referring now toFIG- URE 5, the first material is the core 14 and the second is the skin16. It will be shown how the dimensions of the all-metal designs so fardescribed should be modified when the dielectric material is added.

The effect of the low-K (dielectric constant) core is to decrease thewavelength and impedance in that part of the structure, as indicated inthe transmisison-line diagrams in FIGURE 5. To compensate for this, andthus maintain the same electrical distance, the actual distance from thewires to the metal surface must be changed. The change which compensatesfor the shortened wavelength is approximately:

The change which compensates for the lower impedance is approximately:

81r cos 9 K =dielectric constant of core.

A positive value means that the distance must be increased, and anegative one requires a decrease. Strictly speaking, Formula 12 is validonly at normal incidence. However, for a small departure from normalincidence, the value given by this formula is approximately the averageof the actual values for E-plane and H-plane oblique incidence.Therefore if incidence in both planes is expected, and if the incidenceangle is not too great, this formula yields approximately the bestaverage value. Both formulas are close approximations when the core hasa very low K.

The principal effect of the thin dielectric skin is to introducecapacitive susceptance, as indicated in the transmission-line diagramsin FIGURE 5. For skin thicknesses much smaller than a wavelength, thissusceptance is given by the following approximate formula:

21r T K,- 1) Y0 A B =susceptance of the dielectric skin.

K =dielectric constant of skin. T=thickness of dielectric skin.

small, this new distance may be computed from the following approximateformula:

Combining Formulas 11, 12, 13 and 14, yields the new distance requiredwhen the core and skin are added:

L =distance from metal surface to wire and skin centerline in the designhaving a supporting dielectric core and skin.

Under the conditions mentioned above, this new distance in the compositestructure yields performance closest to an all-metal structure having adistance L. An optimum value for L may be obtained from the relation (Lcos 6=.358 from Equation 8.

It should be appreciated that the design is not limited to wires ofcircular cross-section; any shape having the same inductive susceptancewill do. One alternate construction might utilize printed-circuittechniques to produce wires on the dielectric skin.

The basic property of the twistreflector is to twist a linearlypolarized wave by This occurs when the projections of the elements areat 45 to the incident polarization. However, if the elements are at someother angle, then the polarization is twisted by a different amount; thepolarization twist is actually equal to twice the angle between theelement projections and the incident polarization. Hence, if thetwistreflector is rotated, the polarization of the reflected wave willrotate at twice the speed (at normal incidence).

When a twistreflector is placed in front of an incidentcircularly-polarized wave, the reflected wave is circularly polarizedtoo. This is also the case with an ordinary reflector. However, anordinary reflector reverses the rotational sense of the circularpolarization, while the twistreflector does not. This remains true evenas the twistreflector is rotated.

The principal object of the present invention is to provide atwistreflector intended to twist the polarization of a linearlypolarized wave; this is accomplished by a halfwavelength phase shiftbetween two reflected polarizations. If however, a quarter-wavelengthphase shift were employed, this would yield a device for changing linearpolarization to circular polarization or vice versa; such a design mightbe called a changereflector.

The following invention is claimed:

A twistreflector for electromagnetic radiation of a wavelengthcomprising a plane metal sheet; a plurality of wires embedded in a thindielectric sheet and lying in a plane parallel to said metal sheet; anda dielectirc material of very low dielectric constant substantiallyfilling the space between said plane and said sheet, the diameter ofsaid wire being substantially smaller than the wire to wire spacing, thewire to wire spacing being small with respect to A, and the distancebetween said plane and said sheet being approximately equal to 2 cos 98w cos 9 A cos 9 Sm k in the optimum all-metal design, T is thedielectric skin thickness, K is the dielectric constant of the core, Kis 7 8 -the skin dielectric constant, and 9 is the angle of incidence2,930,039 3/60 Ruze 34375 6 of said radiation. 2,942,266 6/60 Ma'ttingly343756 X References Cited by the Examiner FOREIGN PATENTS UNITED STATESPATENTS 5 668,231 11/ 38 Germany- 9/50 Blitz 343 912 X CHESTER L.JUSTUS, Primary Examiner.

2,554,936 5/51 Burtner 343756

